curve #282

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y² = x³ + x² − 724392592785859978141334075420616x + 7118072780333921924205799244128960519106245831620

a-invariants: [0, 1, 0, -724392592785859978141334075420616, 7118072780333921924205799244128960519106245831620]
rank (lower bound): ≥ 20
torsion subgroup: trivial
conductor (N): 260777211708439416895318114171568806386477713385527932616658460857412039580798160
naive height: 238.6023
Faltings height: 17.8244
discriminant (Δ): 2439625040696707803926966353408296355336554478873072981103670520551170171049918006043404792324019200
primes of bad reduction: 2, 3, 5, 7, 11, 13, 23, 31, 599, 544533839, 11178415412615466013, 417544577316007236807560709864792021583751
regulator: 923781810304140432782.756895299509573170719866337640258961702600976392415666500
submitted by: 7fff-zip
submitted at: 2026-08-22 16:53:59 UTC
last updated: 2026-08-22 16:53:59 UTC

Witness: 20 independent points

(-20497788245595864, -3654337412235387625260786)
(21758808338175949629414/4068289, -15123354791555495587829462217135108/8205738913)
(459390308365849206/25, 13510452788206830291148404/125)
(250931722417936352186037/70123876, -1255563937783724035459206610052391735/587217337624)
(-692149481696280288312/24649, 8924235374902088199567154616070/3869893)
(-905210516577245181360267/59320804, -1746889420172365721120280001535480535/456888832408)
(585425756444396424/49, -140931640614987659363450238/343)
(205104319229317815584466/4818025, 77300952493220460573653708398710936/10575564875)
(28964153386857123258/2809, -128501848105570188959799169080/148877)
(679511110217474390352/3721, 17530135425811416298201356573990/226981)
(6268265097182381366367/1125721, -2155580061804687326441769002633130/1194389981)
(-18820400900020918203306/638401, -861415755895735370079153291731844/510082399)
(76107329795331933/4, 3780174730389576872317965/8)
(-2829976120715387070/289, -17898814406647777417056922680/4913)
(2129572697062746941361011922/60856449481, 74490714162782650551997200131083046512440/15012738378917371)
(-26256237718836027/4, -27235510929755289644788305/8)
(456706330725799875030/18769, -5077290636671092352933304121380/2571353)
(2239350830997435843413208/118875409, 513460761575637735758001389515399170/1296098584327)
(114246578776600062023265744/5479996729, -421045274502040675276094293900050377238/405667717857683)
(26968464344449571248326/1442401, -574903562931748283182103218348284/1732323601)

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